Algebra Examples

$\sqrt{10} \cdot 6 \sqrt{2} - \sqrt[3]{729} \cdot \sqrt[3]{27}$

Step 1

Multiply $\sqrt{10} (6 \sqrt{2})$ .

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Step 1.1

Combine using the product rule for radicals.

$6 \sqrt{10 \cdot 2} - \sqrt[3]{729} \cdot \sqrt[3]{27}$

Step 1.2

Multiply $10$ by $2$ .

$6 \sqrt{20} - \sqrt[3]{729} \cdot \sqrt[3]{27}$

Step 2

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 2.1

Factor $4$ out of $20$ .

$6 \sqrt{4 (5)} - \sqrt[3]{729} \cdot \sqrt[3]{27}$

Step 2.2

Rewrite $4$ as $2^{2}$ .

$6 \sqrt{2^{2} \cdot 5} - \sqrt[3]{729} \cdot \sqrt[3]{27}$

Step 3

Pull terms out from under the radical.

$6 (2 \sqrt{5}) - \sqrt[3]{729} \cdot \sqrt[3]{27}$

Step 4

Multiply $2$ by $6$ .

$12 \sqrt{5} - \sqrt[3]{729} \cdot \sqrt[3]{27}$

Step 5

Rewrite $729$ as $9^{3}$ .

$12 \sqrt{5} - \sqrt[3]{9^{3}} \cdot \sqrt[3]{27}$

Step 6

Pull terms out from under the radical, assuming real numbers.

$12 \sqrt{5} - 1 \cdot 9 \cdot \sqrt[3]{27}$

Step 7

Multiply $- 1$ by $9$ .

$12 \sqrt{5} - 9 \cdot \sqrt[3]{27}$

Step 8

Rewrite $27$ as $3^{3}$ .

$12 \sqrt{5} - 9 \cdot \sqrt[3]{3^{3}}$

Step 9

Pull terms out from under the radical, assuming real numbers.

$12 \sqrt{5} - 9 \cdot 3$

Step 10

Multiply $- 9$ by $3$ .

$12 \sqrt{5} - 27$

Step 11

The result can be shown in multiple forms.

Exact Form:

$12 \sqrt{5} - 27$

Decimal Form:

$- 0.16718427 \dots$